Pseudo-Gaussian and rank-based optimal tests for random individual effects in large small panels

Bennala, Nezar; Hallin, Marc; Paindaveine, Davy

doi:10.1016/j.jeconom.2012.02.008

Cited by 7 publications

(6 citation statements)

References 27 publications

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“…Lemma above and Lemma A.1 in Bennala et al (2012) jointly imply the desired mean square differentiability property. The proof of Proposition 1 is thus complete.…”

Section: Lemmamentioning

confidence: 74%

“…In order to establish the quadratic mean differentiability of q 1 2 µ,β,σ 2 ,b;f1 it is sufficient to show that the four conditions (i)-(iv) of Lemma A.1 in Bennala et al (2012) hold. This last is established in the following Lemma.…”

Section: Discussionmentioning

confidence: 99%

“…In this research, to derive optimal tests, the uniform local asymptotic normality (ULAN) property is established for a class of panel regression models with superdiagonal bilinear time series errors via the quadratic mean differentiability of f 1/2 , where f is the density of ε i,t . This last property (see, Le Cam & Yang, 2000), has recognized success in a variety of testing problems: see, Swensen (1985), Akharif & Hallin (2003), Cassart, Hallin & Paindaveine (2011), Bennala, Hallin & Paindaveine (2012) and Fihri, Akharif, Mellouk & Hallin (2020).…”

Section: Introductionmentioning

confidence: 99%

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Optimal Detection of Bilinear Dependence in Short Panels of Regression Data

Lmakri

Akharif

Mellouk

2020

Rev. colomb. estad.

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In this paper, we propose parametric and nonparametric locally andasymptotically optimal tests for regression models with superdiagonal bilinear time series errors in short panel data (large n, small T). We establish a local asymptotic normality property– with respect to intercept μ, regression coefficient β, the scale parameter σ of the error, and the parameter b of panel superdiagonal bilinear model (which is the parameter of interest)– for a given density f1 of the error terms. Rank-based versions of optimal parametric tests are provided. This result, which allows, by Hájek’s representation theorem, the construction of locally asymptotically optimal rank-based tests for the null hypothesis b = 0 (absence of panel superdiagonal bilinear model). These tests –at specified innovation densities f1– are optimal (most stringent), but remain valid under any actual underlying density. From contiguity, we obtain the limiting distribution of our test statistics under the null and local sequences of alternatives. The asymptotic relative efficiencies, with respect to the pseudo-Gaussian parametric tests, are derived. A Monte Carlo study confirms the good performance of the proposed tests.

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“…Lemma above and Lemma A.1 in Bennala et al (2012) jointly imply the desired mean square differentiability property. The proof of Proposition 1 is thus complete.…”

Section: Lemmamentioning

confidence: 74%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Detection of Bilinear Dependence in Short Panels of Regression Data

Lmakri

Akharif

Mellouk

2020

Rev. colomb. estad.

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“…Chesher (1984) takes the same model assuming U i follows a symmetric location-scale distribution. A more recent treatment, focusing on random individual effects in panel data models by Bennala, Hallin, and Paindaveine (2012) also uses the same reparametrization but adopts a less stringent LeCam framework.…”

Section: Tests For Overdispersion In Poisson Regression Overdispersio...mentioning

confidence: 99%

NEYMAN’S C(α) TEST FOR UNOBSERVED HETEROGENEITY

2015

Econom. Theory

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A unified framework is proposed for tests of unobserved heterogeneity in parametric statistic models based on Neyman's C(α) approach. Such tests are irregular in the sense that the first order derivative of the log likelihood with respect to the heterogeneity parameter is identically zero, and consequently the conventional Fisher information about the parameter is zero. Nevertheless, local asymptotic optimality of the C(α) tests can be established via LeCam's differentiability in quadratic mean and the limit experiment approach. This leads to local alternatives of order n −1/4 . The scalar case result is already familiar from existing literature and we extend it to the multi-dimensional case. The new framework reveals that certain regularity conditions commonly employed in earlier developments are unnecessary, i.e. the symmetry or third moment condition imposed on the heterogeneity distribution. Additionally, the limit experiment for the multi-dimensional case suggests modifications on existing tests for slope heterogeneity in cross sectional and panel data models that lead to power improvement. Since the C(α) framework is not restricted to the parametric model and the test statistics do not depend on the particular choice of the heterogeneity distribution, it is useful for a broad range of applications for testing parametric heterogeneity.

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“…As an alternative to LR-test, Bayesian and permutation test, particularly concerning detecting the randomness in the coefficients of individual effects in longitudinal and clustered data, we present a parametric and non-parametric test locally and asymptotically optimal. Practical examples of a model building using Uniform Local Asymptotic Normality (ULAN) optimal test models can be found in [1,4,10,19] among many others.…”

Section: Introductionmentioning

confidence: 99%

Optimal tests for random effects in linear mixed models

Larbi

Halimi

Akharif

et al. 2021

Hacettepe Journal of Mathematics and Statistics

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In the past decade, mixed-effects modeling has received a great deal of attention in the applied and theoretical statistical literature. They are very flexible tools in analyzing repeated measures, panel data, cross-sectional data, and hierarchical data. However, the complex nature of these models has motivated researchers to study different aspects of this problem. One of which is to test the significance of random effects used to model unobserved heterogeneity in the population. The method of likelihood ratio test based on the normality assumption of the error term and random effects has been proposed. However, this assumption does not necessarily hold in practice. In this paper, we propose an optimal test based on the so-called uniform local asymptotic normality to detect the possible presence of random effects in linear mixed models. We show that the proposed test statistic is, consistent, locally asymptotically optimal even for a model that does not require the traditional assumption of normality and is comparable to the classical L.ratiotest when the standard assumptions are met. Finally, simulation studies and real data analysis are also conducted to empirically examine the performance of this procedure.

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Pseudo-Gaussian and rank-based optimal tests for random individual effects in large small panels

Cited by 7 publications

References 27 publications

Optimal Detection of Bilinear Dependence in Short Panels of Regression Data

Optimal Detection of Bilinear Dependence in Short Panels of Regression Data

NEYMAN’S C(α) TEST FOR UNOBSERVED HETEROGENEITY

Optimal tests for random effects in linear mixed models

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